Example 88.3 Computing Attributable Fraction Estimates

This example computes the excess event risk fraction that is attributable to a specific chemical exposure for workers in a factory.

Suppose that the Factory data set contains the stratum-specific event information for exposure to a specific chemical agent. The variable Age is the grouping variable that forms the strata. The variables Event_E and Count_E indicate the number of events and number of workers for workers with the specific chemical exposure, respectively. The variables Event_NE and Count_NE indicate the number of events and number of workers for workers without the specific chemical exposure, respectively.

data Factory;
input Age $Event_E Count_E Event_NE Count_NE; datalines; 20-29 31 352 143 2626 30-39 57 486 392 4124 40-49 62 538 459 4662 50-59 50 455 337 3622 60-69 38 322 199 2155 70+ 9 68 35 414 ;  The following statements invoke the STDRATE procedure and compute the attributable risk and population attributable risk for the chemical exposure: ods graphics on; proc stdrate data=Factory refdata=Factory method=indirect(af) stat=risk plots(stratum=horizontal) ; population event=Event_E total=Count_E; reference event=Event_NE total=Count_NE; strata Age / stats; run; ods graphics off;  The Standardization Information table in Output 88.3.1 displays the standardization information. Output 88.3.1: Standardization Information The STDRATE Procedure Standardization Information Data Set WORK.FACTORY Reference Data Set WORK.FACTORY Method Indirect Standardization Statistic Risk Number of Strata 6 The STATS option in the STRATA statement requests that the Indirectly Standardized Strata Statistics table in Output 88.3.2 display the strata information and the expected number of events at each stratum. The Expected Events column shows the expected numbers of events when the stratum-specific risks in the reference data set are applied to the corresponding numbers of workers in the study data set. Output 88.3.2: Strata Information (Indirect Standardization) The STDRATE Procedure Indirectly Standardized Strata Statistics Stratum Index Age Study Population Reference Population Expected Events Observed Events Number of Observations Crude Risk Standard Error Number of Observations Crude Risk Value Proportion 95% Normal Confidence Limits Value Proportion 1 20-29 31 352 0.1585 0.088068 0.015105 0.058463 0.117673 2626 0.1492 0.05446 19.1683 2 30-39 57 486 0.2188 0.117284 0.014595 0.088678 0.145890 4124 0.2343 0.09505 46.1959 3 40-49 62 538 0.2422 0.115242 0.013767 0.088260 0.142224 4662 0.2648 0.09846 52.9691 4 50-59 50 455 0.2049 0.109890 0.014662 0.081153 0.138627 3622 0.2058 0.09304 42.3343 5 60-69 38 322 0.1450 0.118012 0.017979 0.082774 0.153251 2155 0.1224 0.09234 29.7346 6 70+ 9 68 0.0306 0.132353 0.041095 0.051809 0.212897 414 0.0235 0.08454 5.7488 With ODS Graphics enabled and the specified STAT=RISK option, the default PLOTS=RISK option displays the stratum-specific risk estimates in the study and reference populations, as shown in Output 88.3.3. The STRATUM=HORIZONTAL global option in the PLOTS option displays the strata information on the horizontal axis. The plot displays the stratum-specific risk estimates in the Indirect Standardized Strata Statistics table in Output 88.3.2. In addition, confidence limits for the risk estimates in the study population and the overall crude risks for the two populations are also displayed Output 88.3.3: Strata Risk Plot The METHOD=INDIRECT option requests that the Standardized Morbidity/Mortality Ratio table in Output 88.3.4 display the SMR, its confidence limits, and the test for the null hypothesis . Output 88.3.4: Standardized Morbidity/Mortality Ratio Standardized Morbidity/Mortality Ratio Observed Events Expected Events SMR Standard Error 95% Normal Confidence Limits Z Pr > |Z| 247 196.151 1.2592 0.0755 1.1113 1.4072 3.43 0.0006 The Standardized Morbidity/Mortality Ratio table shows that SMR=1.259, the confidence limits do not contain the null value SMR=1, and the null hypothesis of SMR=1 is rejected at level from the normal test. The Indirectly Standardized Risk Estimates table in Output 88.3.5 displays the standardized risks and related statistics. Output 88.3.5: Standardized Risks (Indirect Standardization) Indirectly Standardized Risk Estimates Study Population Reference Crude Risk Expected Events SMR Standardized Risk Observed Events Number of Observations Crude Risk Estimate Standard Error 95% Normal Confidence Limits 247 2221 0.1112 0.0889 196.151 1.2592 0.1120 0.00671 0.0988 0.1251 The AF suboption in the METHOD=INDIRECT option requests that the Attributable Fraction Estimates table display the attributable risk and population attributable risk, as shown in Output 88.3.6 Output 88.3.6: Attributable Fraction Estimates Attributable Fraction Estimates Parameter Estimate 95% Confidence Limits Attributable Risk 0.20587 0.10013 0.28937 Population Attributable Risk 0.02806 0.01159 0.04426 The attributable risk fraction 0.206 indicates that of all events in the chemical exposure group are attributed to the chemical exposure, and the population attributable risk fraction 0.028 indicates that about of all events in the total population are attributed to the chemical exposure. The Attributable fraction can also be computed by using Mantel-Haenszel method. Suppose that the Factory1 data set contains the stratum-specific event information for exposure to a specific chemical agent. The variable Age is the grouping variable that forms the strata, and the variable Exposure identifies workers with chemical exposure. The variables Event and Count indicate the number of events and number of workers, respectively. data Factory1; input Exposure$ Age \$ Event Count;
datalines;
Yes  20-29   31   352
Yes  30-39   57   486
Yes  40-49   62   538
Yes  50-59   50   455
Yes  60-69   38   322
Yes  70+      9    68
No   20-29  143  2626
No   30-39  392  4124
No   40-49  459  4662
No   50-59  337  3622
No   60-69  199  2155
No   70+     35   414
;


The following statements invoke the STDRATE procedure and compute the attributable risk and population attributable risk for the chemical exposure:

proc stdrate data=Factory1
method=mh(af)
stat=risk
effect
;
population group(order=data)=Exposure event=Event total=Count;
strata Age;
run;


The Standardization Information table in Output 88.3.7 displays the standardization information.

Output 88.3.7: Standardization Information

The STDRATE Procedure

Standardization Information
Data Set WORK.FACTORY1
Group Variable Exposure
Method Mantel-Haenszel
Statistic Risk
Number of Strata 6

The Mantel-Haenszel Standardized Risk Estimates table in Output 88.3.8 displays the Mantel-Haenszel standardized risks and related statistics.

Output 88.3.8: Standardized Risk Estimates (Mantel-Haenszel Estimation)

Mantel-Haenszel Standardized Risk Estimates
Exposure Study Population Mantel-Haenszel Standardized Risk
Observed
Events
Number of
Observations
Crude
Risk
Expected
Events
Weight Estimate Standard
Error
95% Normal Confidence
Limits
Yes 247 2221 0.1112 219.122 1970.26 0.1112 0.00667 0.0981 0.1243
No 1565 17603 0.0889 174.134 1970.26 0.0884 0.00214 0.0842 0.0926

The EFFECT option requests that the Risk Effect Estimates table display the risk ratio statistic for the two directly standardized risks, as shown in Output 88.3.9.

Output 88.3.9: Mantel-Haenszel Effect Estimates

Risk Effect Estimates
Exposure Risk
Ratio
Log
Risk
Ratio
Standard
Error
Z Pr > |Z|
Yes No
0.1112 0.0884 1.2584 0.2298 0.0647 3.55 0.0004

The AF suboption in the METHOD=MH option requests that the Attributable Fraction Estimates table display the attributable risk and population attributable risk, as shown in Output 88.3.10

Output 88.3.10: Attributable Fraction Estimates

Attributable Fraction Estimates
Parameter Estimate 95% Confidence Limits
Attributable Risk 0.20531 0.09789 0.29994
Population Attributable Risk 0.02799 0.01070 0.04497

Similar to the results of using the SMR estimates, the attributable risk fraction (0.205) indicates that of all events in the chemical exposure group are attributed to the chemical exposure, and the population attributable risk fraction (0.028) indicates that about of all events in the total population are attributed to the chemical exposure.